Meyers

Question 1

Assumption Meyers used for model validation

Answer 1

Generally, the model is validated if the residuals of actual outcome as a % of lognormal model used seem to be uniformly distributed

Question 2

Tests Meyers used to verify the residuals actually follows uniform distribution

Answer 2

Histogram - should be bars of equal heights
p-p plot - sorted predicted percentiles should generally follow 45 degree diagonal line
Kolmogorov-Smirnov Test -
Looks at the maximum distance, if greater than threshold, then reject the test assumption that uniformality exist

Question 3

Mack Model (aka. Chain-Ladder) testing results assuming log-normal mean and std

Answer 3

• 200 triangles in total from 4 LOBs (CommAuto, WC, OL, PA)
• see graph, percentiles show slight uniformity
• Mack model produces a distribution that has lighter tail than lognormal
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Question 4

How to validate a model visually

Answer 4

Question 5

Bootstrap ODP model validation testing results

Answer 5

• the model assumes incremental losses described by odp with mean and var (not lognormal)
• tested on paid triangle

Question 6

Two assumptions Meyers had when determining the models to use

Answer 6

• Mack model assumes last observed losses as fixed, Meyers intend to model it as a r.v.
• Mack assumes incremental losses are i.i.d across all AYs, Meyers allows for correlation

Question 7

What are the MCMC models Meyers used to validate incurred loss data

Answer 7

LCL (Leveled Chain Ladder)
level of each AY is modeled as muw,d = aw + bd
CCL (Correlated Chain Ladder)
allows for correlation on top of LCL, if cor(rho) =0, it’s LCL

Question 8

What are the MCMC models Meyers used to validate paid loss data

Answer 8

CIT (Correlated Incremental Trend)
LIT (Leveled Incremental Trend)
- no detail in paper, similar to CIT but not include AY correlation

Question 9

Model Meyers used to validate cumul loss data

Answer 9

CSR (Changing Settlement Rates) Model

• reflects speedup in claim settlement
• speedup rate 0<r<1 will have mu increase as w increases, which indicates higher settlement rates

Question 10

LCL results

Answer 10

Question 11

CCL results

Answer 11

Question 12

Key improvements CIT to LCL/CCL

Answer 12

CIT includes a calendar year trend (from the inner to outer diagonal along a triangle)
CIT used a mixed lognormal-normal dist to induce skewness and still allow for negative values

Question 13

Describe how CCL simulation process work

Answer 13

For each param set, start with given C1,d and calculate mu2,d

Simulate C-hat-2,d from lognormal(mu2,d, sigma2,d)

Use the result of this simulation to simulate the next ult loss

Do this process 1000 times to form a predictive distribution for each AY and in total

Question 14

How to perform a K-S test

Answer 14

• Sort sample percentiles p by order
• Calculate expected percentile f= (1/sample size)*100
• get the abs difference of p and f
• if the max of all diff > threshold, then test FAILS